I don't think you can do any testing that will give you any pertinent information by using only your antenna, and swapping out the feed line. It can certainly show if there's a difference between them of some kind, but it can't tell you what that difference is. The simplest method I can think of to check a feed line's characteristic impedance is by using a dummy load (which also assumes that the dummy load is accurate). If you use your antenna, you are making an assumption that it is tuned to the 'ideal' 50 ohms and zero reactance, which is impossible to determine with only an SWR meter. Testing usually can do no harm, so if you want to do it, do it.
Considering the short length of the cable I don't see why you would see any differences other than very 'fractional' ones. The biggest differences between those two cables are their characteristic impedance and the amount of loss in the lengths used. The run is short enough that I honestly don't think you could measure those losses at all, the average meter is just not ever accurate enough (any meter!). If you are really hearing a difference, or seeing a difference on a meter of some kind, then that tells me that there's a 'problem' somewhere else. Small differences don't make any -practical- difference.
The routing of the cable shouldn't make any difference at all (keep the stuff off of the muffler or any moving parts!). If the total length of the cable is 'close', as in several feet, that shouldn't make any difference either. Of course, that assumes that the antenna really is 50 ohms and zero reactance, which is rare. The larger that reactance number the more differences there can be. An SWR meter wouldn't know a reactance is it was bitten by it, that's the biggest 'unknown'.
Ain't all this stuff fun??
- 'Doc